In a small saucepan, combine ketchup, vinegar, horseradish, brown sugar, garlic, pepper, and thyme. Bring to boiling over medium heat; reduce heat. Simmer, uncovered, stirring frequently for about 5 minutes or until thickened. Remove from heat. Set aside.
Place the chicken, bone side up, on the unheated rack of a broiler pan. Broil 4 to 5 inches from the heat for about 20 minutes or until lightly browned. Turn chicken. Broil for 5 to 15 minutes more or until chicken is tender and no longer pink. Brush with sauce the last 5 minutes of broiling.
In a grill with a cover, arrange medium-hot coals around a drip pan, then test for medium heat above the pan*. Place chicken, bone side up, on grill rack over drip pan. Cover and grill for 50 to 60 minutes or until chicken is tender and no longer pink, turning once halfway through. Brush often with sauce during the last 10 to 15 minutes of grilling. Makes 4 servings.
For medium heat, you should be able to hold your hand over heat at the height of the food for 4 seconds.